The art has long recognized that acoustical means may be used for determining a portion of the trajectory of a projectile, and the art, generally, has used such acoustical means for locating the point at which a projectile passes into or near a training target for scoring the accuracy of small arms fire, in lieu of the more conventional paper targets. An example of the foregoing is U.S. Pat. No. 4,514,621. Basically, these devices operate by means of a grid of acoustical sensors in which the plane of the sensors is normal to the trajectory of the projectile, e.g. a rifle bullet. As the bullet passes through that grid of sensors, the sensors can locate the passage of the bullet through that grid of sensors by calculating the time delays of the sensors.
Rather than using a grid of acoustical sensors to determine the trajectory of the projectile, curved elongated hoops with acoustical transducers at ends thereof may be used. When a bullet passes within the vicinity of the curved hoops, the position of the bullet passing such curved hoops can be calculated, and U.S. Pat. No. 4,351,026 is representative thereof. Curved hoops may also be used where the target is moving within a defined field normal to the hoops, and U.S. Pat. No. 5,025,424 is representative of that technology.
Somewhat similarly, U.S. Pat. No. 4,885,725 suggests a plurality of triangularly arrayed, mechanically connected acoustical transducers, instead of curved hoops, for determining the point in which a bullet passes the target area and for providing some indication of the velocity of that bullet.
The foregoing patents are, primarily, directed toward training devices for scoring the accuracy of a trainee""s fire. Some patents have addressed determining the general direction of enemy fire toward a military device, such as a helicopter. For example, U.S. Pat. No. 4,659,034 suggests the use of a plurality of transducers disposed on a movable (towed) target and, by use of the transducers, determining the accuracy of fire toward that target. That accuracy of fire includes how close the projectile comes to the towed target (referred to as the miss-distance). U.S. Pat. No. 4,323,993 similarly determines a miss-distance by acoustical transducers, and, particularly, in this patent the miss-distance is calculable even though the projectile misses the towed target altogether.
U.S. Pat. No. 4,805,159 provides a method for estimating the miss-distance between a projectile and a movable training target. In making such estimation, at least a portion of the trajectory of the projectile is also estimated. However, as that patent points out, the estimations of at least a portion of the trajectory of the projectile involves a number of possible estimates of the actual projectile path, and to eliminate erroneous estimates, additional transducers are used for consecutively selecting true estimates from erroneous estimates.
In further developments, U.S. Pat. Nos. 5,544,129, DE 3524753A1, GB 2105464, GB 2181240, and GB 2246861 deal with the detection of acoustic phenomenon for the detection of gunfire. These patents deal with the detection of the muzzle blast wave rather than the projectile shock wave to determine the trajectory of the projectile, such as a bullet. The approximation of a planar wave for the blast wave is made for timing detection.
U.S. Pat. No. 5,930,202 teaches a basic system of two sensors each with at least 3 sensing elements each for trajectory determination. The system senses the shock wave of the projectile. This system has a very large base length (spacing between sensors). As a result, the projectile is assumed to travel parallel to the ground. Consequently, the system is not able to distinguish elevation unless an additional muzzle blast is sensed.
Thus, in general, the prior art, mainly, uses sensors, especially acoustical transducers, in various spatial arrangements for determining the miss-distance of a projectile passing through or near a target. Some of these systems in the art may provide a general direction of a local trajectory of the projectile, but these systems are not capable of providing accurate information as to the entire path of the projectile, and, hence, the position of the source of that projectile. In addition, these prior art systems, whatever their configuration, must have pre-knowledge of the direction and/or the velocity of the projectile, in order to determine the local trajectory of the projectile.
Recently, several attempts have been made to provide a full solution to determining the trajectory of a projectile. For example, U.S. Pat. Nos. 5,258,962, 5,241,518, 4,885,725 and 4,323,993; and foreign patents EP 0,259,428, EP 0064477A, EP 0684485 and WO 91/108876 all provide a full solution by assuming that the portion of the conical shock wave striking a sensor is planar in shape. This leads to an error in the derivation of the direction of arrival of the projectile that becomes more severe as the trajectory miss distance decreases, as is described in more detail below.
As a supersonic projectile passes through the air along its trajectory, it creates a conical shock wave. The conical shock wave extends outward from the bow or tip of the projectile. As the shock wave expands out from the projectile""s trajectory, it encounters the sensors. In order to locate the trajectory in three-dimensional space, relevant acoustic systems all make the same fundamental assumption; they assume that the sensing elements within each sensor are spaced close to each other compared to the distance between the sensor and the trajectory. This allows the subsequent assumption that the segment of the shock wave hitting an individual sensor (and its associated elements) is a flat planar wave. As the trajectory has a smaller miss distance to a sensor, this planar assumption leads to an increasing error in the trajectory location and orientation determination. If the sensor is part of a target system, this will lead to increased target hitpoint errors. This error arises because the actual segment of the shock cone striking the sensor is curved. This discrepancy between the flat and curved shock wave shapes leads to the generation of a unit pointing vector that is misaligned from the true unit pointing vector. This, in turn, causes a misalignment of the deduced trajectory and any projected hitpoint.
Accordingly, it is currently the general practice to assume a planar shock wave strikes the sensor. The normal to that assumed plane can then calculated from the arrival time differences at the sensor elements. This works well when the approximation to the shock wave segment is closer to a plane in shape than to a cone. This, therefore, is a good approximation when the shock source (trajectory) is far from the sensor. But as greater accuracy is required, it is necessary to eliminate this planar approximation and calculate from the exact conical geometry of the shock wave, regardless of any other errors.
Therefore, there is a need to remove the above described errors created by the planar approximation of the shock wave. Furthermore, there is a need to achieve a best fit to all sensor data; thus, minimizing intrinsic timing, mechanical alignment and mechanical construction errors (non-curvature based errors).
The present invention can provide a method and apparatus for determining the trajectory of a projectile. As the projectile moves through the air, a pressure wave is created. The pressure wave is detected and various parameters can be determined based on this detection. An incorrect trajectory can be determined from these parameters using a planar approximation for the pressure wave. In an exemplary embodiment of the invention, the correct trajectory of the projectile can be generated based on the incorrect trajectory and the measured parameters. Unit pointing vectors used to generate the incorrect trajectory can be perturbed to minimize a difference between the parameters actually measured and parameters calculated using a correct geometry for the pressure wave and the incorrect trajectory. As the difference between the measured parameters and the calculated parameters falls within an acceptable range, a more accurate trajectory for the projectile can be determined.
Given a trajectory and unit pointing vectors determined based on a planar or other approximation of a shock wave, a method and apparatus according to an embodiment of the invention may calculate parameters, such as times, the sensors should have detected, based on this trajectory and a conical geometry for the shock wave. A difference between the calculated times and the actual times measured by the sensors may be minimized. The minimization may be performed by perturbing the unit pointing vectors. When the perturbation of the unit pointing vectors results in an acceptable difference between the calculated times and the measured times, an accurate trajectory of the projectile can be generated from the perturbed unit pointing vectors.
In an exemplary embodiment, an apparatus for determining a trajectory of a projectile comprises at least two spaced apart sensors capable of encountering a pressure wave generated by a projectile and capable of generating signals in response to the pressure wave, the signals being related to a unit pointing vector. Means for calculating the unit pointing vectors for each of the sensors from the signals may also be provided. Means for calculating a first trajectory of the projectile based on the unit pointing vectors and means for back-calculating times from the first trajectory based on a conical geometry of the pressure wave may also be provided.
According to another embodiment, a method for determining the trajectory of a projectile comprises detecting a shock wave created by the projectile with a number of sensors. Times at which the sensors encounter the shock wave may be measured. Unit pointing vectors can be generated based on the measured times. A first trajectory for the projectile can be determined based on the unit pointing vectors. At least one of the unit pointing vectors may be perturbed. A second trajectory can be generated based on the perturbed unit pointing vector and the remaining unit pointing vectors. Calculated times may be determined based on the second trajectory. A difference between the measured times and the calculated times can be determined. If the difference is outside an acceptable range, the process may be repeated. Otherwise a source of the projectile may be located based on the second trajectory.